Circuit Complexity From Supersymmetric Quantum Field Theory With Morse Function
arXiv:2101.12582 · doi:10.3390/sym14081656
Abstract
Computation of circuit complexity has gained much attention in the Theoretical Physics community in recent times to gain insights into the chaotic features and random fluctuations of fields in the quantum regime. Recent studies of circuit complexity take inspiration from Nielsen's geometric approach, which is based on the idea of optimal quantum control in which a cost function is introduced for the various possible path to determine the optimum circuit. In this paper, we study the relationship between the circuit complexity and Morse theory within the framework of algebraic topology, which will then help us study circuit complexity in supersymmetric quantum field theory describing both simple and inverted harmonic oscillators up to higher orders of quantum corrections. We will restrict ourselves to supersymmetry with one fermionic generator . The expression of circuit complexity in quantum regime would then be given by the Hessian of the Morse function in supersymmetric quantum field theory. We also provide technical proof of the well known universal connecting relation between quantum chaos and circuit complexity of the supersymmetric quantum field theories, using the general description of Morse theory.
arXiv comment41 pages, 10 figures, 4 tables, This project is the part of the non-profit virtual international research consortium "Quantum Aspects of Space-Time and Matter (QASTM)", Revised version, References and some of the explanations elaborated and updated, Accepted for publication in Symmetry
References in corpus (60)
- The Large N Limit of Superconformal Field Theories and Supergravity
- A bound on chaos
- Black holes and the butterfly effect
- Cool horizons for entangled black holes
- Building up spacetime with quantum entanglement
- The Unruh effect and its applications
- Complexity Equals Action
- Localized shocks
- Complexity, action, and black holes
- Chaos and complexity by design
- Circuit complexity in quantum field theory
- Towards Complexity for Quantum Field Theory States
- Gravitational Dynamics From Entanglement "Thermodynamics"
- The Second Law of Quantum Complexity
- Hall viscosity, orbital spin, and geometry: paired superfluids and quantum Hall systems
- Supergravity as Generalised Geometry I: Type II Theories
- Out-of-time-order correlators in quantum mechanics
- Circuit Complexity in Fermionic Field Theory
- More on Supersymmetric and 2d Analogs of the SYK Model
- Quantum Complexity and Negative Curvature
- Enhancement of Supersymmetry via Renormalization Group Flow and the Superconformal Index
- Supersymmetric SYK model and random matrix theory
- Holographic Pseudo Entropy
- Universality of Gravity from Entanglement
- Does Complexity Equal Anything?
- Circuit Complexity for Coherent States
- Switchbacks and the Bridge to Nowhere
- Notes on Melonic Tensor Models
- Islands and complexity of eternal black hole and radiation subsystems for a doubly holographic model
- A Complexity for Quantum Field Theory States and Application in Thermofield Double States
- Complexity for Conformal Field Theories in General Dimensions
- The Multi-faceted Inverted Harmonic Oscillator: Chaos and Complexity
- Bell violation in the Sky
- Physics of the Inverted Harmonic Oscillator: From the lowest Landau level to event horizons
- Superspace, or One thousand and one lessons in supersymmetry
- Time Dependence of Holographic Complexity in Gauss-Bonnet Gravity
- Entangled de Sitter from Stringy Axionic Bell pair I: An analysis using Bunch Davies vacuum
- Quantum entanglement in de Sitter space from Stringy Axion: An analysis using vacua
- Holographic Complexity of Quantum Black Holes
- Open Quantum Entanglement: A study of two atomic system in static patch of de Sitter space
- D-term Triggered Dynamical Supersymmetry Breaking
- Quantum aspects of chaos and complexity from bouncing cosmology: A study with two-mode single field squeezed state formalism
- Circuit Complexity as a novel probe of Quantum Entanglement: A study with Black Hole Gas in arbitrary dimensions
- The Generalized OTOC from Supersymmetric Quantum Mechanics: Study of Random Fluctuations from Eigenstate Representation of Correlation Functions
- Cosmological spectrum of two-point correlation function from vacuum fluctuation of Stringy Axion field in De Sitter space: A study of the role of Quantum Entanglement
- Wilson Renormalization Group for Supersymmetric Gauge Theories and Gauge Anomalies
- Quantum Scrambling and State Dependence of the Butterfly Velocity
- Quantum Out-of-Equilibrium Cosmology
- On subregion action complexity in AdS and in the BTZ black hole
- A Generalized Momentum/Complexity Correspondence
- Hints of Gravitational Ergodicity: Berry's Ensemble and the Universality of the Semi-Classical Page Curve
- Chaos and Complexity from Quantum Neural Network: A study with Diffusion Metric in Machine Learning
- Supersymmetry in Particle Physics: The Renormalization Group Viewpoint
- Cambridge Lectures on Supersymmetry and Extra Dimensions
- Schwinger-Keldysh path integral for the quantum harmonic oscillator
- Holographic complexity of the electromagnetic black hole
- TASI 2008 Lectures: Introduction to Supersymmetry and Supersymmetry Breaking
- The geometry of quantum computation
- Introduction to Supersymmetric Gauge Theories
- Four-dimensional geometric supergravity and electromagnetic duality: a brief guide for mathematicians